Geometric Transforms

The Wolfram Language's symbolic architecture and sophisticated mathematical capabilities allow it to take a uniquely high-level approach to geometric transformationssupporting complete geometric, matrix, and functional representations in any number of dimensions, whether for mechanical systems, computer graphics, or pure mathematics.

Geometric Object Transformations

Rotate  ▪  Translate  ▪  Scale

GeometricTransformation apply any transformation function to geometric objects

Rotation Matrices in 3D

EulerMatrix axis-oriented rotations in the current frame (intrinsic rotations)

RollPitchYawMatrix axis-oriented rotations in the global frame (extrinsic rotations)

EulerAngles, RollPitchYawAngles gives angles from rotation matrices

Transformation Matrices in nD

RotationMatrix rotations in any number of dimensions

ScalingMatrix stretch or shrink along any direction

ShearingMatrix  ▪  ReflectionMatrix  ▪  IdentityMatrix

TransformationMatrix the matrix representation of a transformation function

Symbolic Transformation Functions in nD

RotationTransform  ▪  TranslationTransform  ▪  ScalingTransform

ShearingTransform  ▪  ReflectionTransform  ▪  RescalingTransform

AffineTransform  ▪  LinearFractionalTransform

TransformationFunction general symbolic representation of transformations

Composition symbolic composition of transformation functions

InverseFunction inverse of transformation functions

Transformation Functions from Points

FindGeometricTransform find affine or linear fractional transform between point sets

Algebraic Structure

FiniteGroupData properties of finite groups